It’s fundamentally language specific, so any comprehensive solution is going to need to interface with the localization system. Really, names should be keyed by (user, language, tag) triples, where the localization defines the acceptable tags based on language requirements. For example, a single person may need their name stored as:

  en:disp     Eric
  is:disp:nf  Eiríkur
  is:disp:þf  Eirík
  is:disp:þgf Eiríki
  is:disp:ef  Eiríks

Designing a UI to collect this information is left as an exercise for the reader.

Since asking a user to enter every possible variant is unwieldy and without doing so, the problem is unsolvable, I’ll stick with my original suggestion of using a single field. Yes, some names will break, but far fewer than if first and last names are required.